<<Does the fact that something can't be precisely measured automatically mean that its not determined? >>
Perhaps there is a different way for you to look it that is more familiar and intuitive to you... when you throw a pot, no matter how accurately you did it, no matter how accurate the proportions, no matter how carefully you cool it, it is not deterministic if it cracks or not from any a priori measurements anyone can make. It doesn't have to do with not measuring accurately.
That is what the uncertainty principle means - there are tons of experiments that prove it - ones where all the components can be weighed absolutely - heck, we can move one atom at a time, but despite that, you simply can't predict how it will turn out with 100% certainty.
Radioactive decay is a really good example. Or rolling a die. You simply can't make a machine that will drop a die from a reasonable height, with rotation, and have it generate a 100% predictable outcome. Or a pachinko machine. You could stack all the ball bearings in exactly the same order, each perfectly round, but when you opened the gate, they simply won't act the same way the each time. There would be general trends in all of these examples. Things would tend to do certain things, but would never do it EXACTLY the same way. |
